Beilinson's Conjectures on Special Values of L-Functions

✍ Scribed by M. Rapoport, N. Schappacher, P. Schneider

• Publisher: Academic Press
• Year: 1988
• Tongue: English
• Leaves: 385
• Series: Perspectives in Mathematics Vol 4
• Category: Library

✦ Synopsis

Beilinsons Conjectures on Special Values of L-Functions deals with Alexander Beilinsons conjectures on special values of L-functions. Topics covered range from Pierre Delignes conjecture on critical values of L-functions to the Deligne-Beilinson cohomology, along with the Beilinson conjecture for algebraic number fields and Riemann-Roch theorem. Beilinsons regulators are also compared with those of Émile Borel.

Comprised of 10 chapters, this volume begins with an introduction to the Beilinson conjectures and the theory of Chern classes from higher k-theory. The "simplest" example of an L-function is presented, the Riemann zeta function. The discussion then turns to Delignes conjecture on critical values of L-functions and its connection to Beilinsons version. Subsequent chapters focus on the Deligne-Beilinson cohomology; ?-rings and Adams operations in algebraic k-theory; Beilinson conjectures for elliptic curves with complex multiplication; and Beilinsons theorem on modular curves. The book concludes by reviewing the definition and properties of Deligne homology, as well as Hodge-D-conjecture.

This monograph should be of considerable interest to researchers and graduate students who want to gain a better understanding of Beilinsons conjectures on special values of L-functions.

✦ Table of Contents

Content:
Front Matter, Page iii
Copyright, Page iv
Preface, Page v, M. Rapoport, N. Schappacher, P. Schneider
Einladung zur Arbeitsgemeinschaft in Oberwolfach über “Die Beilinson-Vermutung”, Pages ix-xvi
Teilnehmerliste, Page xvii
Contributors, Pages xix-xx
Introduction to the Beilinson conjectures, Pages 1-35, Peter Schneider
Deligne's Conjecture, Pages 37-42, Maria Heep, Uwe Weselmann
DELIGNE-BEILINSON COHOMOLOGY, Pages 43-91, Hélène Esnault, Eckart Viehweg
λ-Rings and Adams operations in algebraic K-theory, Pages 93-102, WOLFGANG K. SEILER
THE THEOREM OF RIEMANN-ROCH, Pages 103-168, GÜNTER TAMME
Comparison of the regulators of Beilinson and of Borel, Pages 169-192, M. Rapoport
The Beilinson Conjecture for Algebraic Number Fields, Pages 193-247, Jürgen Neukirch
On the Beilinson conjectures for elliptic curves with complex multiplication, Pages 249-272, Christopher Deninger, Kay Wingberg
BEILINSON'S THEOREM ON MODULAR CURVES, Pages 273-304, Norbert Schappacher, Anthony J. Scholl
Deligne homology, Hodge-D-conjecture, and motives, Pages 305-372, Uwe Jannsen
Addresses of authors, Page 373
Perspectives in Mathematics, Page ibc1